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Organizers:
Douglas N. Arnold  Institute for Mathematics and its Applications  arnold@ima.umn.edu 
Abhay Ashtekar  Center for Gravitational Wave Physics, Penn State  ashtekar@gravity.phys.psu.edu 
Pablo Laguna  Center for Gravitational Wave Physics, Penn State  pablo@astro.psu.edu 
Description:
The numerical solution of Einstein's equations of general relativity promises to become one of the most potent tools for for understanding the complex behavior of strong dynamical gravitational fields. In recent years the field of numerical relativity has grown substantially, engaging the efforts of large groups of researchers across the globe. Despite some promising results, the development of accurate, efficient, and validated algorithms for Einstein's equations remains elusive. This is in part due to the size and complexity of the equations, but also due to fundamental issues which remain to be fully understood.
The problems of numerical relativity share many features with other large scale problems of computational physics, and it is highly likely that lessons learned in fields such as computational fluid dynamics, solid mechanics, and electromagnetics will help advance numerical relativity. But the fundamental differences between general relativity and classical field theories also bring major new computational issues.
This workshop will bring together numerical relativists and mathematicians working in fields such as numerical analysis, scientific computation, partial differential equations, and geometry, for an intense but informal period aimed at maximal communication and interaction between diverse researchers. The primary goals are to bring new ideas and techniques into the numerical relativity community and to propel applied mathematicians with relevant skills and interests into NR. We hope that this workshop will lead to continued interactions which could take place at many venues such as the Center for Gravitational Wave Physics at Penn State, the Institute for Theoretical Physics at UC Santa Barbara, the Caltech Visitors Program in the Numerical Simulation of Gravitational Wave Sources, and the IMA. Such interactions can lay the foundation for the formation of multidisciplinary teams better equipped to tackle the challenges of numerical relativity.
The workshop will focus on a few of the many issues in numerical relativity, selected for their importance, mathematical nature, and relative accessibility. Main among these are the initial value problem of vacuum relativity, including the encoding as partial differential equations; discretization techniques for these equations; treatment of black hole spacetimes; the imposition of boundary conditions; and the determination of physically relevant initial data.
Monday  Tuesday  Saturday 
MONDAY,
JUNE 24 All talks are in Lecture Hall EE/CS 3180 unless otherwise noted. 


Introduction to GR for computational scientists, with an emphasis on the vacuum field equations and issues like geometric wellposedness; PDE formulations; initial value problems; gauge freedom, etc. This will be most directed at the participants who have not had much to do with GR in the past, but will also serve to set a common vocabulary for the remainder of the week. The day will end with a reception at which all participants are invited to display posters.  
8:30 am  Coffee and Registration 
Reception Room EE/CS 3176 

9:00 am  Douglas Arnold, Fadil Santosa, and Lee Samuel Finn  Welcome and Introduction  
9:1010:00 am  Douglas N. Arnold  
10:0010:30 am  Discussion  
10:3011:00 am  Break  Reception Room EE/CS 3176  
11:0011:50 am  Alan
D. Rendall AlbertEinsteinInstitut 

11:50 am12:30 pm  Discussion  
12:302:30 pm 
Break


2:303:20 pm  Robert
Bartnik University of Canberra 

3:204:00 pm  Discussion  
4:006:00 pm  Reception and Posters  IMA East, 400 Lind Hall  
TUESDAY,
JUNE
25 All talks are in Lecture Hall EE/CS 3180 unless otherwise noted. 

The morning will focus on key ideas from better developed areas of computational science: electromagnetics and hyperbolic systems from other applications. The afternoon will focus on formulations of GR for computation.  
8:30 am  Coffee  Reception Room EE/CS 3176  
9:009:50 am  Ralf
Hiptmair IAM, Universitaet Bonn 

9:5010:30 am  Discussion  
10:3011:00 am  Break  Reception Room EE/CS 3176  
11:0011:50 am  Eitan
Tadmor University of California Los Angeles 
Computational Methods for Hyperbolic Systems. Preservation of Global and Local Invariants (pdf)  
11:50 am12:30 pm  Discussion  
12:302:30 pm 
Break


2:303:00 pm  Oscar
Reula FaMAF, Universidad Nacional de Cordoba 

3:00 3:30 pm  Discussion  
3:303:45 pm  Break  Reception Room EE/CS 3176  
3:454:15 pm  Manuel
Tiglio Louisiana State University 

4:154:45 pm  Discussion  
WEDNESDAY,
JUNE
26 All talks are in Lecture Hall EE/CS 3180 unless otherwise noted. 

The morning will extend the tutorials of the first day to issues involving black holes and horizons. The remaining talks will focus on the main conceptual and numerical challenges in numerical relativity. During dinner there will be the possibility for any participants with relevant software and computations to demonstrate to do so.  
8:30 am  Coffee  Reception Room EE/CS 3176  
9:009:50 am  Jeff
Winicour University of Pittsburgh 
Black hole spacetimes slides.html notes (ps) 

9:5010:30 am  Discussion  
10:3011:00 am  Break  Reception Room EE/CS 3176  
11:0011:50 am  Matthew
W. Choptuik University of British Columbia 

11:50 am12:30 pm  Discussion  
12:302:30 pm 
Break


2:303:20 pm  Pablo
Laguna Penn State University 

3:204:00 pm  Discussion  
5:308:00 pm  Pizza
Dinner/Computational Demonstrations, Lind
Hall 409 The following brief presentations will be given:


THURSDAY,
JUNE
27 All talks are in Lecture Hall EE/CS 3180 unless otherwise noted. 

The day will focus on some particular challenges and promising techniques for numerical relativity.  
8:30 am  Coffee  Reception Room EE/CS 3176  
9:009:30 am  Gregory
B. Cook Wake Forest University 

9:309:50 am  Discussion  
9:5010:05 am  Break  Reception Room EE/CS 3176  
10:0510:35 am  Michael J. Holst University of California, San Diego 

10:3510:55 am  Discussion  
10:5511:10 am  Break  Reception Room EE/CS 3176  
11:10 am11:25 pm  Markus
Keel University of Minnesota 
Linear degeneracy of the Einstein 

11:2511:40 am  Discussion  
11:4011:55 am  Eitan
Tadmor University of California Los Angeles 
Remarks on first order formulations  
11:55 am 12:10 pm  Discussion  
12:102:30 pm  Break  
2:30 3:00 pm  Deirdre
Shoemaker Penn State University 

3:003:30 pm  Discussion  
3:303:45 pm  Break  Reception Room EE/CS 3176  
3:454:15 pm  Mark
A. Scheel California Institute of Technology 

4:15 4:45 pm  Discussion  
FRIDAY,
JUNE
28 All talks are in Lecture Hall EE/CS 3180 unless otherwise noted. 

The day will again focus on some particular challenges facing numerical relativity and promising techniques.  
8:30 am  Coffee  Reception Room EE/CS 3176  
9:009:50 am  Luis
Lehner University of British Columbia 
Outer boundary conditions  
9:5010:30 am  Discussion  
9:5010:05 am  Break  Reception Room EE/CS 3176  
10:0510:35 am  Richard
S. Falk Rutgers University 
Overview of finite element methods for linear hyperbolic problems 

10:3510:55 am  Discussion  
10:5511:10 am  Break  Reception Room EE/CS 3176  
11:1011:25 am  Lee
Lindblom Caltech 
Energy norms and stability of the Einstein equations  
11:25 am11:40 pm  Discussion  
11:4011:55 am  Sasha
Husa AlbertEinsteinInstitut 
The conformal approach 

11:55 am12:10 pm  Discussion  
12:102:00 pm  Lee
Samuel Finn Penn State University and Lee Lindblom Caltech 
Lunchtime
discussion on gravitational wave phenomenology 

2:00 4:00 pm  Panel discussion on numerical methods  
4:00 4:15 pm  Break  Reception Room EE/CS 3176  
4:15 4:30 pm  Discussion  
6:15 pm  Workshop
Dinner Radisson shuttle to Kikugawa at 6:00 pm 
Kikugawa
Restaurant 43 Main Street S.E., Minneapolis 

SATURDAY,
JUNE 29 All talks are in Lecture Hall EE/CS 3180 unless otherwise noted. 

The workshop will conclude with discussions and summary presentations assessing what was learned and future directions.  
9:0010:30 am 
Discussion lead by Richard Price (University of Utah), Ragnar Winther (University of Oslo) and Beverly Berger (NSF) Richard Price slides.html 

10:3011:00 pm  Break  
11:00 am 12:30 pm  Discussion, continued  

Monday  Tuesday  Saturday 
Name  Department  Affiliation 

Douglas N. Arnold  Institute for Mathematics and its Applications  
Robert Bartnik  Mathematics and Statistics  University of Canberra 
Beverly Berger  Division of Physics  National Science Foundation 
David Brown  Physics  North Carolina State University 
Matt Choptuik  Physics  University of British Columbia 
Gregory B. Cook  Physics  Wake Forest University 
Rick Falk  Mathematics  Rutgers University 
Lee Samuel Finn  Director, Center for Gravitational Wave Physics  Penn State University 
Jörg Frauendiener  Theoretische Astrophysik  Universität Tübingen 
Ralf Hiptmair  Mathematics  University of Tübingen 
Michael Holst  Mathematics  UC San Diego 
Sascha Husa  MaxPlanckInstitut für Gravitationsphysik  AlbertEinsteinInstitut 
Marcus Keel  Mathematics  University of Minnesota 
Pablo Laguna  Center for Gravitational Wave Physics  Penn State University 
Luis Lehner  Physics & Astronomy  University of British Columbia 
Lee Lindblom  Physics, Math & Astronomy  Caltech 
Peter Monk  Mathematical Sciences  University of Delaware 
Arup Mukherjee  Mathematics Sciences  Montclair State University 
Denis Pollney  MaxPlanckInstitut für Gravitationsphysik  AlbertEinsteinInstitut 
Richard Price  Physics  University of Utah 
Alan Rendall  MaxPlanckInstitut für Gravitationsphysik  AlbertEinsteinInstitut 
Oscar Reula  Investigador Independiente, CONICET  FaMAF, Universidad Nacional de Cordoba 
Mark A. Scheel  Physics, Mathematics, and Astronomy  California Institute of Technology 
Deirdre Shoemaker  Astronomy  Penn State University 
Eitan Tadmor  Mathematics  University of California Los Angeles 
Blake Temple  Mathematics  University of California 
Manuel Tiglio  Physics  Louisiana State University 
Jeff Winicour  Physics  University of Pittsburgh 
Ragnar Winther  Informatics  University of Oslo 
Jinchao Xu  Mathematics  Pennsylvania State University 
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